arXiv math/00101282000-10-12math.FA

Two characterizations of the standard unit vector basis of $l_1$

David Mitra

备注：: Latex. 8 pgs

英文摘要：

We show that for a sequence in a Banach space, the property of being stable under large perturbations characterizes the property of being equivalent to the unit vector basis of $l_1$. We show that a normalized unconditional basic sequence in $l_1$ that is semi-normalized in $l_\infty$ is equivalent to the standard unit vector basis of~$l_1$.

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